Search

The paper presents a numerical analysis of the rolling contact between an elastic ellipsoid and an elastic-plastic flat. Numerical simulations have been performed with the help of a contact solver called Plast-Kid[R], with an algorithm based on an integral formulation or semi-analytical method. The application of both the conjugate gradient method and the discrete convolution and fast Fourier transform technique allows keeping the computing time reasonable when performing transient 3D simulations while solving the contact problem and calculating the subsurface stress and strain states. The effects of the ellipticity ratio k--ranging from 1 to 16--and of the normal load--from 4.2 GPa to 8 GPa--are investigated. The reference simulation corresponds to the rolling of a ceramic ball on a steel plate made of an AISI 52100 bearing steel under a load of 5.7 GPa. The results that are presented are, first, the permanent deformation of the surface and, second, the contact pressure distribution, the von Mises stress field, the hydrostatic pressure, and the equivalent plastic strain state within the elastic-plastic body. A comparison with an experimental surface deformation profile is also given to validate the theoretical background and the numerical procedure. [DOI: 10.1115/1.2768078] Keywords: contact modeling, elastic-plastic contact, plasticity, overload, permanent print, semianalytical method

A three-dimensional numerical model based on a semianalytical method in the framework of small strains and small displacements is presented for solving an elastic-plastic contact with surface traction. A Coulomb's law is assumed for the friction, as commonly used for sliding contacts. The effects of the contact pressure distribution and residual strain on the geometry of the contacting surfaces are derived from Betti's reciprocal theorem with initial strain. The main advantage of this approach over the classical finite element method (FEM) is the computing time, which is reduced by several orders of magnitude. The contact problem, which is one of the most time-consuming procedures in the elastic-plastic algorithm, is obtained using a method based on the variational principle and accelerated by means of the discrete convolution fast Fourier transform (FFT) and conjugate gradient methods. The FFT technique is also involved in the calculation of internal strains and stresses. A return-mapping algorithm with an elastic predictor/plastic corrector scheme and avon Mises criterion is used in the plasticity loop. The model is first validated by comparison with results obtained by the FEM. The effect of the friction coefficient on the contact pressure distribution, subsurface stress field, and residual strains is also presented and discussed. [DOI: 10.1115/1.2768076] Keywords: elastic-plastic contact, SAM method, contact mechanics, stress analysis, dry contact

A semi-analytical method for the tridimensional elastic-plastic contact between two hemispherical asperities is proposed. The first part of the paper describes the algorithm used to deal with the normal contact, which can be either load-driven or displacement-driven (dd). Both formulations use the conjugate gradient method and the discrete convolution and fast Fourier transform (DC-FFT) technique. A validation of the code is made in the case of the displacement-driven formulation for an elastic-plastic body in contact with a rigid punch, simulating a nano-indentation test. Another new feature is the treatment of the contact between two elastic-plastic bodies. The model is first validated through comparison with the finite element method. The contact pressure distribution, the hydrostatic pressure and the equivalent plastic strain state below the contacting surfaces are also found to be strongly modified in comparison to the case of an elastic-plastic body in contact with a purely elastic body. The way to consider rolling and sliding motion of the contacting bodies consists of solving the elastic-plastic contact at each time step while upgrading the geometries as well as the hardening state along the moving directions. The derivations concerning the interference calculation at each step of the sliding process are then shown, and an application to the tugging between two spherical asperities in simple sliding (dd formulation) is made. The way to project the forces in the global reference is outlined, considering the macro-projection due to the angle between the plane of contact and the sliding direction, and the micro-projection due to the pile-up induced by the permanent deformation of the bodies due to their relative motion. Finally, a load ratio is introduced and results are presented in terms of forces, displacements, and energy loss in the contact. [DOI: 10.1115/1.2464137] Keywords: contact modeling, elastic-plastic contact, SAM method, tangential and normal loading, sliding

A semi-analytical thermo-elastic-plastic contact model has been recently developed and presented in a companion paper. The main advantage of this approach over the classical finite element method (FEM) is the treatment of transient problems with the use of fine meshing and the possibility of studying the effect of a surface defect on the surface deflection as well as on subsurface stress state. A return-mapping algorithm with an elastic predictor/plastic corrector scheme and avon Mises criterion is now used, which improves the plasticity loop. This improvement in the numerical algorithm increases the computing speed significantly and shows a much better convergence and accuracy. The contact model is validated through a comparison with the FEM results of Kogut and Etsion (2002, J. Appl. Mech., 69, pp. 657-662) which correspond to the axisymmetric contact between an elastic-perfectly plastic sphere and a rigid fiat. A model for wear prediction based on the material removal during cyclic loading is then proposed. Results are presented, first, for initially smooth surfaces and, second, for rough surfaces. The effects of surface shear stress and hardening law are underlined. [DOI: 10.1115/1.2163360]

The stress field within machine components is an important indicator for contact failures. Since both thermal stresses due to frictional heating and plasticity are significant in engineering application, it is critical to predict the total stress field. In this work, the steady-state thermal effect is considered and a thermo-elastic--plastic contact model is developed. The model is applicable for rolling and/or sliding contact problem, as far as small equivalent plastic strain hypothesis is respected. Influence coefficients for surface normal displacement, temperature, and strain and stress tensors are used with the discrete convolution and fast Fourier transform algorithm. The single-loop conjugate gradient iteration scheme is also applied to achieve fast convergence speed. Simulations are presented for several academic examples ranging from elastic to thermo-elastic--plastic. The thermo-elastic--plastic analyses show that the heat factor in a contact situation has significant effect not only on the critical Hertzian pressure and on the pressure distribution, but also on the magnitude and depth of the maximum von Mises stress during loading and the residual ones found after unloading. [DOI: 10.1115/1.1843851]